What is the integral from 0 to pi/4 of cos(6x) ?

The integral from 0 to pi/4 of cos(6x) is -1/6

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integral from 0 to pi/4 of cos(6x)

\int_{0}^{\frac{π}{4}} cos (6 x) d x

- \frac{1}{6}

Decimal

- 0.16666 \dots

Solution steps

\int_{0}^{\frac{π}{4}} cos (6 x) d x

Apply u-substitution

= \int_{0}^{\frac{3 π}{2}} cos (u) \frac{1}{6} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{6} \cdot \int_{0}^{\frac{3 π}{2}} cos (u) d u

Use the common integral:

\int cos (u) d u = sin (u)

= \frac{1}{6} [sin (u)]_{0}^{\frac{3 π}{2}}

Compute the boundaries:

- 1

= \frac{1}{6} (- 1)

Simplify

= - \frac{1}{6}

What is the integral from 0 to pi/4 of cos(6x) ?
The integral from 0 to pi/4 of cos(6x) is -1/6